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Decision analysis is an effective method for a consultant to communicate the logic behind a recommended solution because it provides a structured approach to evaluating alternatives based on their potential outcomes and impacts. This method employs a systematic evaluation of decisions, allowing stakeholders to see the rationale behind the recommendation clearly.

Through decision analysis, the consultant presents various options, assesses the associated risks and benefits, and uses quantitative and qualitative analysis to demonstrate how a particular solution best addresses organizational goals and criteria. This level of detail not only clarifies the consultant's thought process but also enhances stakeholder understanding and facilitates informed decision-making.

In contrast, while options like feasibility studies and use case models contribute valuable insights, they do not specifically focus on the logic underpinning a decision. Feasibility studies emphasize whether a solution is practical, whereas use case models illustrate how a solution will be used but don't delve deeply into decision-making processes. The DATA framework helps organize information but may not provide the depth of analysis that decision analysis offers. Thus, decision analysis serves best to communicate the reasoning and justification behind the recommended course of action.